LMFDB - Embedded newform 253.3.c.a.208.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [253,3,Mod(208,253)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("253.208"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(253, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 253 = 11 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	253.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.89375068832$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			208.4
Character	$\chi$	$=$	253.208
Dual form			253.3.c.a.208.41

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.43881i q^{2} +2.25129 q^{3} -7.82541 q^{4} -5.97558 q^{5} -7.74175i q^{6} +7.31000i q^{7} +13.1548i q^{8} -3.93171 q^{9} +20.5489i q^{10} +(-5.54238 + 9.50168i) q^{11} -17.6172 q^{12} -2.03096i q^{13} +25.1377 q^{14} -13.4527 q^{15} +13.9354 q^{16} -12.6026i q^{17} +13.5204i q^{18} +7.17039i q^{19} +46.7613 q^{20} +16.4569i q^{21} +(32.6745 + 19.0592i) q^{22} -4.79583 q^{23} +29.6153i q^{24} +10.7075 q^{25} -6.98408 q^{26} -29.1130 q^{27} -57.2037i q^{28} -4.59018i q^{29} +46.2614i q^{30} -28.3774 q^{31} +4.69829i q^{32} +(-12.4775 + 21.3910i) q^{33} -43.3378 q^{34} -43.6815i q^{35} +30.7672 q^{36} -0.432206 q^{37} +24.6576 q^{38} -4.57227i q^{39} -78.6078i q^{40} -55.0369i q^{41} +56.5921 q^{42} +28.4614i q^{43} +(43.3714 - 74.3546i) q^{44} +23.4942 q^{45} +16.4919i q^{46} -65.8869 q^{47} +31.3725 q^{48} -4.43608 q^{49} -36.8211i q^{50} -28.3720i q^{51} +15.8931i q^{52} +75.3874 q^{53} +100.114i q^{54} +(33.1189 - 56.7780i) q^{55} -96.1619 q^{56} +16.1426i q^{57} -15.7848 q^{58} +30.5593 q^{59} +105.273 q^{60} -14.3773i q^{61} +97.5844i q^{62} -28.7408i q^{63} +71.8980 q^{64} +12.1362i q^{65} +(73.5596 + 42.9077i) q^{66} -121.469 q^{67} +98.6202i q^{68} -10.7968 q^{69} -150.212 q^{70} -51.5776 q^{71} -51.7210i q^{72} +77.8507i q^{73} +1.48627i q^{74} +24.1057 q^{75} -56.1112i q^{76} +(-69.4573 - 40.5148i) q^{77} -15.7232 q^{78} +109.661i q^{79} -83.2719 q^{80} -30.1563 q^{81} -189.261 q^{82} -121.206i q^{83} -128.782i q^{84} +75.3076i q^{85} +97.8732 q^{86} -10.3338i q^{87} +(-124.993 - 72.9092i) q^{88} +64.2205 q^{89} -80.7921i q^{90} +14.8463 q^{91} +37.5293 q^{92} -63.8856 q^{93} +226.572i q^{94} -42.8472i q^{95} +10.5772i q^{96} -31.2577 q^{97} +15.2548i q^{98} +(21.7910 - 37.3579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) $ 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/253\mathbb{Z}\right)^\times$.

$n$	$24$	$166$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	3.43881i		−	1.71940i	−0.510795	−	0.859702i	$-0.670649\pi$
$2$		−	3.43881i		−	1.71940i	0.510795	−	0.859702i	$-0.329351\pi$
$3$	2.25129			0.750429			0.375214	−	0.926938i	$-0.377569\pi$
$3$	2.25129			0.750429			0.375214	+	0.926938i	$0.377569\pi$
$4$	−7.82541			−1.95635
$5$	−5.97558			−1.19512			−0.597558	−	0.801826i	$-0.703862\pi$
$5$	−5.97558			−1.19512			−0.597558	+	0.801826i	$0.703862\pi$
$6$		−	7.74175i		−	1.29029i
$7$			7.31000i			1.04429i	0.852858	+	0.522143i	$0.174867\pi$
$7$			7.31000i			1.04429i	−0.852858	+	0.522143i	$0.825133\pi$
$8$			13.1548i			1.64436i
$9$	−3.93171			−0.436856
$10$			20.5489i			2.05489i
$11$	−5.54238	+	9.50168i	−0.503853	+	0.863790i
$11$	−5.54238	+	9.50168i	−0.503853	+	0.863790i
$12$	−17.6172			−1.46810
$13$		−	2.03096i		−	0.156228i	−0.996944	−	0.0781139i	$-0.975110\pi$
$13$		−	2.03096i		−	0.156228i	0.996944	−	0.0781139i	$-0.0248898\pi$
$14$	25.1377			1.79555
$15$	−13.4527			−0.896849
$16$	13.9354			0.870961
$17$		−	12.6026i		−	0.741328i	−0.928767	−	0.370664i	$-0.879130\pi$
$17$		−	12.6026i		−	0.741328i	0.928767	−	0.370664i	$-0.120870\pi$
$18$			13.5204i			0.751133i
$19$			7.17039i			0.377389i	0.982036	+	0.188694i	$0.0604256\pi$
$19$			7.17039i			0.377389i	−0.982036	+	0.188694i	$0.939574\pi$
$20$	46.7613			2.33807
$21$			16.4569i			0.783662i
$22$	32.6745	+	19.0592i	1.48520	+	0.866327i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$			29.6153i			1.23397i
$25$	10.7075			0.428300
$26$	−6.98408			−0.268619
$27$	−29.1130			−1.07826
$28$		−	57.2037i		−	2.04299i
$29$		−	4.59018i		−	0.158282i	−0.996863	−	0.0791411i	$-0.974782\pi$
$29$		−	4.59018i		−	0.158282i	0.996863	−	0.0791411i	$-0.0252178\pi$
$30$			46.2614i			1.54205i
$31$	−28.3774			−0.915399			−0.457700	−	0.889107i	$-0.651327\pi$
$31$	−28.3774			−0.915399			−0.457700	+	0.889107i	$0.651327\pi$
$32$			4.69829i			0.146822i
$33$	−12.4775	+	21.3910i	−0.378106	+	0.648213i
$34$	−43.3378			−1.27464
$35$		−	43.6815i		−	1.24804i
$36$	30.7672			0.854645
$37$	−0.432206			−0.0116813			−0.00584063	−	0.999983i	$-0.501859\pi$
$37$	−0.432206			−0.0116813			−0.00584063	+	0.999983i	$0.501859\pi$
$38$	24.6576			0.648884
$39$		−	4.57227i		−	0.117238i
$40$		−	78.6078i		−	1.96519i
$41$		−	55.0369i		−	1.34236i	−0.741293	−	0.671181i	$-0.765787\pi$
$41$		−	55.0369i		−	1.34236i	0.741293	−	0.671181i	$-0.234213\pi$
$42$	56.5921			1.34743
$43$			28.4614i			0.661892i	0.943650	+	0.330946i	$0.107368\pi$
$43$			28.4614i			0.661892i	−0.943650	+	0.330946i	$0.892632\pi$
$44$	43.3714	−	74.3546i	0.985713	−	1.68988i
$45$	23.4942			0.522094
$46$			16.4919i			0.358521i
$47$	−65.8869			−1.40185			−0.700924	−	0.713236i	$-0.747229\pi$
$47$	−65.8869			−1.40185			−0.700924	+	0.713236i	$0.747229\pi$
$48$	31.3725			0.653594
$49$	−4.43608			−0.0905323
$50$		−	36.8211i		−	0.736421i
$51$		−	28.3720i		−	0.556314i
$52$			15.8931i			0.305636i
$53$	75.3874			1.42240			0.711202	−	0.702988i	$-0.248151\pi$
$53$	75.3874			1.42240			0.711202	+	0.702988i	$0.248151\pi$
$54$			100.114i			1.85396i
$55$	33.1189	−	56.7780i	0.602162	−	1.03233i
$56$	−96.1619			−1.71718
$57$			16.1426i			0.283204i
$58$	−15.7848			−0.272151
$59$	30.5593			0.517954			0.258977	−	0.965883i	$-0.416615\pi$
$59$	30.5593			0.517954			0.258977	+	0.965883i	$0.416615\pi$
$60$	105.273			1.75455
$61$		−	14.3773i		−	0.235693i	−0.993032	−	0.117847i	$-0.962401\pi$
$61$		−	14.3773i		−	0.235693i	0.993032	−	0.117847i	$-0.0375991\pi$
$62$			97.5844i			1.57394i
$63$		−	28.7408i		−	0.456203i
$64$	71.8980			1.12341
$65$			12.1362i			0.186710i
$66$	73.5596	+	42.9077i	1.11454	+	0.650117i
$67$	−121.469			−1.81298			−0.906488	−	0.422233i	$-0.861247\pi$
$67$	−121.469			−1.81298			−0.906488	+	0.422233i	$0.861247\pi$
$68$			98.6202i			1.45030i
$69$	−10.7968			−0.156475
$70$	−150.212			−2.14589
$71$	−51.5776			−0.726445			−0.363222	−	0.931702i	$-0.618324\pi$
$71$	−51.5776			−0.726445			−0.363222	+	0.931702i	$0.618324\pi$
$72$		−	51.7210i		−	0.718347i
$73$			77.8507i			1.06645i	0.845974	+	0.533224i	$0.179020\pi$
$73$			77.8507i			1.06645i	−0.845974	+	0.533224i	$0.820980\pi$
$74$			1.48627i			0.0200848i
$75$	24.1057			0.321409
$76$		−	56.1112i		−	0.738305i
$77$	−69.4573	−	40.5148i	−0.902043	−	0.526166i
$78$	−15.7232			−0.201579
$79$			109.661i			1.38811i	0.719920	+	0.694057i	$0.244178\pi$
$79$			109.661i			1.38811i	−0.719920	+	0.694057i	$0.755822\pi$
$80$	−83.2719			−1.04090
$81$	−30.1563			−0.372300
$82$	−189.261			−2.30806
$83$		−	121.206i		−	1.46031i	−0.683279	−	0.730157i	$-0.739447\pi$
$83$		−	121.206i		−	1.46031i	0.683279	−	0.730157i	$-0.260553\pi$
$84$		−	128.782i		−	1.53312i
$85$			75.3076i			0.885972i
$86$	97.8732			1.13806
$87$		−	10.3338i		−	0.118780i
$88$	−124.993	−	72.9092i	−1.42038	−	0.828513i
$89$	64.2205			0.721579			0.360790	−	0.932647i	$-0.382507\pi$
$89$	64.2205			0.721579			0.360790	+	0.932647i	$0.382507\pi$
$90$		−	80.7921i		−	0.897690i
$91$	14.8463			0.163146
$92$	37.5293			0.407928
$93$	−63.8856			−0.686942
$94$			226.572i			2.41034i
$95$		−	42.8472i		−	0.451023i
$96$			10.5772i			0.110179i
$97$	−31.2577			−0.322244			−0.161122	−	0.986934i	$-0.551511\pi$
$97$	−31.2577			−0.322244			−0.161122	+	0.986934i	$0.551511\pi$
$98$			15.2548i			0.155662i
$99$	21.7910	−	37.3579i	0.220111	−	0.377352i
$100$	−83.7906			−0.837906
$101$			35.0785i			0.347312i	0.984806	+	0.173656i	$0.0555581\pi$
$101$			35.0785i			0.347312i	−0.984806	+	0.173656i	$0.944442\pi$
$102$	−97.5659			−0.956528
$103$	−115.766			−1.12394			−0.561969	−	0.827158i	$-0.689956\pi$
$103$	−115.766			−1.12394			−0.561969	+	0.827158i	$0.689956\pi$
$104$	26.7170			0.256894
$105$		−	98.3395i		−	0.936566i
$106$		−	259.243i		−	2.44569i
$107$		−	114.288i		−	1.06811i	−0.845450	−	0.534055i	$-0.820668\pi$
$107$		−	114.288i		−	1.06811i	0.845450	−	0.534055i	$-0.179332\pi$
$108$	227.821			2.10945
$109$			95.0212i			0.871754i	0.900006	+	0.435877i	$0.143562\pi$
$109$			95.0212i			0.871754i	−0.900006	+	0.435877i	$0.856438\pi$
$110$	−195.249	−	113.890i	−1.77499	−	1.03536i
$111$	−0.973020			−0.00876595
$112$			101.868i			0.909532i
$113$	−53.2784			−0.471490			−0.235745	−	0.971815i	$-0.575753\pi$
$113$	−53.2784			−0.471490			−0.235745	+	0.971815i	$0.575753\pi$
$114$	55.5113			0.486941
$115$	28.6579			0.249199
$116$			35.9201i			0.309656i
$117$			7.98514i			0.0682491i
$118$		−	105.088i		−	0.890572i
$119$	92.1248			0.774158
$120$		−	176.969i		−	1.47474i
$121$	−59.5640	−	105.324i	−0.492265	−	0.870446i
$122$	−49.4408			−0.405252
$123$		−	123.904i		−	1.00735i
$124$	222.065			1.79084
$125$	85.4059			0.683247
$126$	−98.8341			−0.784397
$127$			227.726i			1.79312i	0.442921	+	0.896561i	$0.353942\pi$
$127$			227.726i			1.79312i	−0.442921	+	0.896561i	$0.646058\pi$
$128$		−	228.450i		−	1.78477i
$129$			64.0747i			0.496703i
$130$	41.7339			0.321030
$131$			195.620i			1.49328i	0.665227	+	0.746641i	$0.268335\pi$
$131$			195.620i			1.49328i	−0.665227	+	0.746641i	$0.731665\pi$
$132$	97.6414	−	167.393i	0.739708	−	1.26813i
$133$	−52.4155			−0.394102
$134$			417.710i			3.11724i
$135$	173.967			1.28864
$136$	165.785			1.21901
$137$	88.4178			0.645385			0.322693	−	0.946504i	$-0.395412\pi$
$137$	88.4178			0.645385			0.322693	+	0.946504i	$0.395412\pi$
$138$			37.1281i			0.269044i
$139$		−	54.8474i		−	0.394585i	−0.980345	−	0.197293i	$-0.936785\pi$
$139$		−	54.8474i		−	0.394585i	0.980345	−	0.197293i	$-0.0632149\pi$
$140$			341.825i			2.44161i
$141$	−148.330			−1.05199
$142$			177.365i			1.24905i
$143$	19.2975	+	11.2564i	0.134948	+	0.0787158i
$144$	−54.7898			−0.380485
$145$			27.4290i			0.189165i
$146$	267.714			1.83366
$147$	−9.98690			−0.0679381
$148$	3.38219			0.0228526
$149$			2.58929i			0.0173778i	0.999962	+	0.00868889i	$0.00276579\pi$
$149$			2.58929i			0.0173778i	−0.999962	+	0.00868889i	$0.997234\pi$
$150$		−	82.8948i		−	0.552632i
$151$		−	207.408i		−	1.37356i	−0.726864	−	0.686782i	$-0.759023\pi$
$151$		−	207.408i		−	1.37356i	0.726864	−	0.686782i	$-0.240977\pi$
$152$	−94.3254			−0.620562
$153$			49.5496i			0.323854i
$154$	−139.323	+	238.850i	−0.904693	+	1.55098i
$155$	169.571			1.09401
$156$			35.7799i			0.229358i
$157$	153.280			0.976304			0.488152	−	0.872759i	$-0.337671\pi$
$157$	153.280			0.976304			0.488152	+	0.872759i	$0.337671\pi$
$158$	377.103			2.38673
$159$	169.719			1.06741
$160$		−	28.0750i		−	0.175469i
$161$		−	35.0575i		−	0.217749i
$162$			103.702i			0.640134i
$163$	−144.158			−0.884408			−0.442204	−	0.896915i	$-0.645803\pi$
$163$	−144.158			−0.884408			−0.442204	+	0.896915i	$0.645803\pi$
$164$			430.686i			2.62613i
$165$	74.5602	−	127.824i	0.451880	−	0.774689i
$166$	−416.805			−2.51087
$167$			53.8084i			0.322206i	0.986938	+	0.161103i	$0.0515051\pi$
$167$			53.8084i			0.322206i	−0.986938	+	0.161103i	$0.948495\pi$
$168$	−216.488			−1.28862
$169$	164.875			0.975593
$170$	258.968			1.52334
$171$		−	28.1919i		−	0.164865i
$172$		−	222.722i		−	1.29489i
$173$		−	127.989i		−	0.739824i	−0.929067	−	0.369912i	$-0.879388\pi$
$173$		−	127.989i		−	0.739824i	0.929067	−	0.369912i	$-0.120612\pi$
$174$	−35.5360			−0.204230
$175$			78.2718i			0.447268i
$176$	−77.2352	+	132.410i	−0.438836	+	0.752327i
$177$	68.7977			0.388688
$178$		−	220.842i		−	1.24069i
$179$	−209.111			−1.16822			−0.584109	−	0.811675i	$-0.698556\pi$
$179$	−209.111			−1.16822			−0.584109	+	0.811675i	$0.698556\pi$
$180$	−183.852			−1.02140
$181$	204.831			1.13166			0.565831	−	0.824521i	$-0.308556\pi$
$181$	204.831			1.13166			0.565831	+	0.824521i	$0.308556\pi$
$182$		−	51.0537i		−	0.280515i
$183$		−	32.3674i		−	0.176871i
$184$		−	63.0884i		−	0.342872i
$185$	2.58268			0.0139604
$186$			219.690i			1.18113i
$187$	119.746	+	69.8482i	0.640351	+	0.373520i
$188$	515.592			2.74251
$189$		−	212.816i		−	1.12601i
$190$	−147.343			−0.775491
$191$	267.508			1.40057			0.700284	−	0.713865i	$-0.253057\pi$
$191$	267.508			1.40057			0.700284	+	0.713865i	$0.253057\pi$
$192$	161.863			0.843037
$193$		−	190.029i		−	0.984605i	−0.870424	−	0.492302i	$-0.836155\pi$
$193$		−	190.029i		−	0.984605i	0.870424	−	0.492302i	$-0.163845\pi$
$194$			107.489i			0.554069i
$195$			27.3220i			0.140113i
$196$	34.7142			0.177113
$197$		−	305.377i		−	1.55014i	−0.631876	−	0.775069i	$-0.717715\pi$
$197$		−	305.377i		−	1.55014i	0.631876	−	0.775069i	$-0.282285\pi$
$198$	−128.467	−	74.9352i	−0.648821	−	0.378460i
$199$	243.849			1.22537			0.612687	−	0.790326i	$-0.290089\pi$
$199$	243.849			1.22537			0.612687	+	0.790326i	$0.290089\pi$
$200$			140.856i			0.704278i
$201$	−273.462			−1.36051
$202$	120.628			0.597170
$203$	33.5542			0.165292
$204$			222.022i			1.08835i
$205$			328.877i			1.60428i
$206$			398.096i			1.93251i
$207$	18.8558			0.0910909
$208$		−	28.3022i		−	0.136068i
$209$	−68.1308	−	39.7410i	−0.325985	−	0.190148i
$210$	−338.171			−1.61034
$211$		−	280.012i		−	1.32707i	−0.748145	−	0.663536i	$-0.769055\pi$
$211$		−	280.012i		−	1.32707i	0.748145	−	0.663536i	$-0.230945\pi$
$212$	−589.937			−2.78272
$213$	−116.116			−0.545145
$214$	−393.013			−1.83651
$215$		−	170.073i		−	0.791037i
$216$		−	382.977i		−	1.77304i
$217$		−	207.439i		−	0.955938i
$218$	326.760			1.49890
$219$			175.264i			0.800293i
$220$	−259.169	+	444.311i	−1.17804	+	2.01960i
$221$	−25.5953			−0.115816
$222$			3.34603i			0.0150722i
$223$	−297.141			−1.33247			−0.666235	−	0.745742i	$-0.732095\pi$
$223$	−297.141			−1.33247			−0.666235	+	0.745742i	$0.732095\pi$
$224$	−34.3445			−0.153324
$225$	−42.0988			−0.187106
$226$			183.214i			0.810682i
$227$			249.276i			1.09813i	0.835779	+	0.549066i	$0.185016\pi$
$227$			249.276i			1.09813i	−0.835779	+	0.549066i	$0.814984\pi$
$228$		−	126.322i		−	0.554046i
$229$	−431.863			−1.88586			−0.942932	−	0.332986i	$-0.891944\pi$
$229$	−431.863			−1.88586			−0.942932	+	0.332986i	$0.891944\pi$
$230$		−	98.5489i		−	0.428473i
$231$	−156.368	−	91.2104i	−0.676919	−	0.394850i
$232$	60.3832			0.260272
$233$			138.106i			0.592728i	0.955075	+	0.296364i	$0.0957741\pi$
$233$			138.106i			0.592728i	−0.955075	+	0.296364i	$0.904226\pi$
$234$	27.4594			0.117348
$235$	393.712			1.67537
$236$	−239.139			−1.01330
$237$			246.878i			1.04168i
$238$		−	316.799i		−	1.33109i
$239$			328.222i			1.37332i	0.726981	+	0.686658i	$0.240923\pi$
$239$			328.222i			1.37332i	−0.726981	+	0.686658i	$0.759077\pi$
$240$	−187.469			−0.781120
$241$		−	151.578i		−	0.628956i	−0.949265	−	0.314478i	$-0.898171\pi$
$241$		−	151.578i		−	0.628956i	0.949265	−	0.314478i	$-0.101829\pi$
$242$	−362.189	+	204.829i	−1.49665	+	0.846402i
$243$	194.126			0.798874
$244$			112.508i			0.461099i
$245$	26.5082			0.108197
$246$	−426.082			−1.73204
$247$	14.5628			0.0589586
$248$		−	373.300i		−	1.50524i
$249$		−	272.870i		−	1.09586i
$250$		−	293.695i		−	1.17478i
$251$	−359.160			−1.43092			−0.715458	−	0.698655i	$-0.753782\pi$
$251$	−359.160			−1.43092			−0.715458	+	0.698655i	$0.753782\pi$
$252$			224.908i			0.892493i
$253$	26.5803	−	45.5685i	0.105061	−	0.180113i
$254$	783.108			3.08310
$255$			169.539i			0.664859i
$256$	−498.005			−1.94533
$257$	−82.1597			−0.319687			−0.159844	−	0.987142i	$-0.551099\pi$
$257$	−82.1597			−0.319687			−0.159844	+	0.987142i	$0.551099\pi$
$258$	220.341			0.854033
$259$		−	3.15943i		−	0.0121986i
$260$		−	94.9704i		−	0.365271i
$261$			18.0473i			0.0691466i
$262$	672.700			2.56756
$263$			337.482i			1.28320i	0.767039	+	0.641601i	$0.221729\pi$
$263$			337.482i			1.28320i	−0.767039	+	0.641601i	$0.778271\pi$
$264$	−281.396	−	164.139i	−1.06589	−	0.621740i
$265$	−450.483			−1.69994
$266$			180.247i			0.677620i
$267$	144.579			0.541494
$268$	950.547			3.54682
$269$	49.3183			0.183339			0.0916697	−	0.995789i	$-0.470780\pi$
$269$	49.3183			0.183339			0.0916697	+	0.995789i	$0.470780\pi$
$270$		−	598.239i		−	2.21570i
$271$			386.698i			1.42693i	0.700691	+	0.713465i	$0.252875\pi$
$271$			386.698i			1.42693i	−0.700691	+	0.713465i	$0.747125\pi$
$272$		−	175.622i		−	0.645667i
$273$	33.4233			0.122430
$274$		−	304.052i		−	1.10968i
$275$	−59.3451	+	101.739i	−0.215800	+	0.369961i
$276$	84.4893			0.306121
$277$		−	28.1561i		−	0.101647i	−0.998708	−	0.0508233i	$-0.983815\pi$
$277$		−	28.1561i		−	0.101647i	0.998708	−	0.0508233i	$-0.0161845\pi$
$278$	−188.610			−0.678452
$279$	111.572			0.399898
$280$	574.623			2.05222
$281$		−	41.5314i		−	0.147798i	−0.997266	−	0.0738992i	$-0.976456\pi$
$281$		−	41.5314i		−	0.147798i	0.997266	−	0.0738992i	$-0.0235443\pi$
$282$			510.079i			1.80879i
$283$			86.3755i			0.305214i	0.988287	+	0.152607i	$0.0487668\pi$
$283$			86.3755i			0.305214i	−0.988287	+	0.152607i	$0.951233\pi$
$284$	403.616			1.42118
$285$		−	96.4613i		−	0.338461i
$286$	38.7085	−	66.3606i	0.135344	−	0.232030i
$287$	402.320			1.40181
$288$		−	18.4723i		−	0.0641399i
$289$	130.175			0.450433
$290$	94.3231			0.325252
$291$	−70.3701			−0.241822
$292$		−	609.213i		−	2.08635i
$293$			214.375i			0.731655i	0.930683	+	0.365827i	$0.119214\pi$
$293$			214.375i			0.731655i	−0.930683	+	0.365827i	$0.880786\pi$
$294$			34.3430i			0.116813i
$295$	−182.609			−0.619015
$296$		−	5.68561i		−	0.0192081i
$297$	161.355	−	276.622i	0.543284	−	0.931389i
$298$	8.90407			0.0298794
$299$			9.74014i			0.0325757i
$300$	−188.637			−0.628789
$301$	−208.052			−0.691204
$302$	−713.237			−2.36171
$303$			78.9718i			0.260633i
$304$			99.9221i			0.328691i
$305$			85.9126i			0.281681i
$306$	170.392			0.556836
$307$			203.287i			0.662173i	0.943600	+	0.331086i	$0.107415\pi$
$307$			203.287i			0.662173i	−0.943600	+	0.331086i	$0.892585\pi$
$308$	543.532	+	317.045i	1.76471	+	1.02937i
$309$	−260.622			−0.843436
$310$		−	583.123i		−	1.88104i
$311$	−489.326			−1.57340			−0.786698	−	0.617338i	$-0.788211\pi$
$311$	−489.326			−1.57340			−0.786698	+	0.617338i	$0.788211\pi$
$312$	60.1476			0.192781
$313$	192.073			0.613652			0.306826	−	0.951766i	$-0.400733\pi$
$313$	192.073			0.613652			0.306826	+	0.951766i	$0.400733\pi$
$314$		−	527.100i		−	1.67866i
$315$			171.743i			0.545215i
$316$		−	858.142i		−	2.71564i
$317$	−324.085			−1.02235			−0.511176	−	0.859476i	$-0.670790\pi$
$317$	−324.085			−1.02235			−0.511176	+	0.859476i	$0.670790\pi$
$318$		−	583.630i		−	1.83531i
$319$	43.6145	+	25.4405i	0.136723	+	0.0797509i
$320$	−429.632			−1.34260
$321$		−	257.294i		−	0.801540i
$322$	−120.556			−0.374398
$323$	90.3653			0.279769
$324$	235.985			0.728350
$325$		−	21.7465i		−	0.0669123i
$326$			495.733i			1.52065i
$327$			213.920i			0.654189i
$328$	724.002			2.20732
$329$		−	481.633i		−	1.46393i
$330$	−439.561	−	256.398i	−1.33200	−	0.776964i
$331$	−638.017			−1.92754			−0.963772	−	0.266728i	$-0.914057\pi$
$331$	−638.017			−1.92754			−0.963772	+	0.266728i	$0.914057\pi$
$332$			948.487i			2.85689i
$333$	1.69931			0.00510303
$334$	185.037			0.554003
$335$	725.849			2.16671
$336$			229.333i			0.682539i
$337$		−	4.76839i		−	0.0141495i	−0.999975	−	0.00707476i	$-0.997748\pi$
$337$		−	4.76839i		−	0.0141495i	0.999975	−	0.00707476i	$-0.00225199\pi$
$338$		−	566.974i		−	1.67744i
$339$	−119.945			−0.353820
$340$		−	589.313i		−	1.73327i
$341$	157.278	−	269.633i	0.461227	−	0.790712i
$342$	−96.9465			−0.283469
$343$			325.762i			0.949744i
$344$	−374.405			−1.08839
$345$	64.5170			0.187006
$346$	−440.131			−1.27206
$347$		−	354.696i		−	1.02218i	−0.859527	−	0.511090i	$-0.829242\pi$
$347$		−	354.696i		−	1.02218i	0.859527	−	0.511090i	$-0.170758\pi$
$348$			80.8664i			0.232375i
$349$			562.820i			1.61266i	0.591463	+	0.806332i	$0.298551\pi$
$349$			562.820i			1.61266i	−0.591463	+	0.806332i	$0.701449\pi$
$350$	269.162			0.769034
$351$			59.1273i			0.168454i
$352$	−44.6417	−	26.0397i	−0.126823	−	0.0739764i
$353$	161.827			0.458432			0.229216	−	0.973376i	$-0.426384\pi$
$353$	161.827			0.458432			0.229216	+	0.973376i	$0.426384\pi$
$354$		−	236.582i		−	0.668311i
$355$	308.206			0.868185
$356$	−502.552			−1.41166
$357$	207.399			0.580950
$358$			719.093i			2.00864i
$359$			406.019i			1.13097i	0.824757	+	0.565487i	$0.191312\pi$
$359$			406.019i			1.13097i	−0.824757	+	0.565487i	$0.808688\pi$
$360$			309.063i			0.858508i
$361$	309.586			0.857578
$362$		−	704.374i		−	1.94578i
$363$	−134.096	−	237.114i	−0.369410	−	0.653208i
$364$	−116.178			−0.319172
$365$		−	465.203i		−	1.27453i
$366$	−111.305			−0.304113
$367$	553.390			1.50788			0.753938	−	0.656946i	$-0.228152\pi$
$367$	553.390			1.50788			0.753938	+	0.656946i	$0.228152\pi$
$368$	−66.8317			−0.181608
$369$			216.389i			0.586420i
$370$		−	8.88135i		−	0.0240036i
$371$			551.082i			1.48540i
$372$	499.931			1.34390
$373$			371.964i			0.997223i	0.866826	+	0.498611i	$0.166156\pi$
$373$			371.964i			0.997223i	−0.866826	+	0.498611i	$0.833844\pi$
$374$	240.195	−	411.782i	0.642232	−	1.10102i
$375$	192.273			0.512728
$376$		−	866.732i		−	2.30514i
$377$	−9.32248			−0.0247281
$378$	−731.833			−1.93607
$379$	−396.427			−1.04598			−0.522991	−	0.852338i	$-0.675184\pi$
$379$	−396.427			−1.04598			−0.522991	+	0.852338i	$0.675184\pi$
$380$			335.297i			0.882360i
$381$			512.677i			1.34561i
$382$		−	919.910i		−	2.40814i
$383$	307.243			0.802200			0.401100	−	0.916034i	$-0.368628\pi$
$383$	307.243			0.802200			0.401100	+	0.916034i	$0.368628\pi$
$384$		−	514.307i		−	1.33934i
$385$	415.047	+	242.099i	1.07805	+	0.628829i
$386$	−653.473			−1.69293
$387$		−	111.902i		−	0.289152i
$388$	244.604			0.630424
$389$	−513.353			−1.31967			−0.659837	−	0.751409i	$-0.729375\pi$
$389$	−513.353			−1.31967			−0.659837	+	0.751409i	$0.729375\pi$
$390$	93.9550			0.240910
$391$			60.4398i			0.154577i
$392$		−	58.3560i		−	0.148867i
$393$			440.397i			1.12060i
$394$	−1050.13			−2.66532
$395$		−	655.287i		−	1.65896i
$396$	−170.524	+	292.340i	−0.430615	+	0.738233i
$397$	279.794			0.704771			0.352385	−	0.935855i	$-0.385371\pi$
$397$	279.794			0.704771			0.352385	+	0.935855i	$0.385371\pi$
$398$		−	838.552i		−	2.10691i
$399$	−118.002			−0.295745
$400$	149.213			0.373033
$401$	−724.982			−1.80793			−0.903967	−	0.427602i	$-0.859358\pi$
$401$	−724.982			−1.80793			−0.903967	+	0.427602i	$0.859358\pi$
$402$			940.385i			2.33927i
$403$			57.6333i			0.143011i
$404$		−	274.504i		−	0.679465i
$405$	180.201			0.444941
$406$		−	115.387i		−	0.284204i
$407$	2.39545	−	4.10669i	0.00588563	−	0.0100901i
$408$	373.229			0.914778
$409$			57.8826i			0.141522i	0.997493	+	0.0707611i	$0.0225428\pi$
$409$			57.8826i			0.141522i	−0.997493	+	0.0707611i	$0.977457\pi$
$410$	1130.95			2.75840
$411$	199.054			0.484316
$412$	905.914			2.19882
$413$			223.388i			0.540892i
$414$		−	64.8415i		−	0.156622i
$415$			724.276i			1.74524i
$416$	9.54204			0.0229376
$417$		−	123.477i		−	0.296108i
$418$	−136.662	+	234.289i	−0.326942	+	0.560499i
$419$	−506.877			−1.20973			−0.604866	−	0.796328i	$-0.706773\pi$
$419$	−506.877			−1.20973			−0.604866	+	0.796328i	$0.706773\pi$
$420$			769.546i			1.83225i
$421$	−367.915			−0.873907			−0.436954	−	0.899484i	$-0.643943\pi$
$421$	−367.915			−0.873907			−0.436954	+	0.899484i	$0.643943\pi$
$422$	−962.908			−2.28177
$423$	259.048			0.612406
$424$			991.710i			2.33894i
$425$		−	134.942i		−	0.317511i
$426$			399.301i			0.937325i
$427$	105.098			0.246131
$428$			894.348i			2.08960i
$429$	43.4443	+	25.3413i	0.101269	+	0.0590706i
$430$	−584.848			−1.36011
$431$			563.137i			1.30658i	0.757107	+	0.653291i	$0.226612\pi$
$431$			563.137i			1.30658i	−0.757107	+	0.653291i	$0.773388\pi$
$432$	−405.700			−0.939121
$433$	−400.443			−0.924812			−0.462406	−	0.886668i	$-0.653014\pi$
$433$	−400.443			−0.924812			−0.462406	+	0.886668i	$0.653014\pi$
$434$	−713.342			−1.64364
$435$			61.7505i			0.141955i
$436$		−	743.580i		−	1.70546i
$437$		−	34.3880i		−	0.0786910i
$438$	602.700			1.37603
$439$			51.4207i			0.117132i	0.998284	+	0.0585658i	$0.0186527\pi$
$439$			51.4207i			0.117132i	−0.998284	+	0.0585658i	$0.981347\pi$
$440$	746.906	+	435.674i	1.69751	+	0.990169i
$441$	17.4414			0.0395496
$442$			88.0174i			0.199134i
$443$	−194.355			−0.438725			−0.219363	−	0.975643i	$-0.570398\pi$
$443$	−194.355			−0.438725			−0.219363	+	0.975643i	$0.570398\pi$
$444$	7.61428			0.0171493
$445$	−383.755			−0.862370
$446$			1021.81i			2.29105i
$447$			5.82923i			0.0130408i
$448$			525.574i			1.17316i
$449$	341.728			0.761087			0.380544	−	0.924763i	$-0.375737\pi$
$449$	341.728			0.761087			0.380544	+	0.924763i	$0.375737\pi$
$450$			144.770i			0.321710i
$451$	522.943	+	305.035i	1.15952	+	0.676353i
$452$	416.925			0.922400
$453$		−	466.935i		−	1.03076i
$454$	857.212			1.88813
$455$	−88.7153			−0.194979
$456$	−212.353			−0.465687
$457$		−	296.786i		−	0.649423i	−0.945813	−	0.324712i	$-0.894733\pi$
$457$		−	296.786i		−	0.649423i	0.945813	−	0.324712i	$-0.105267\pi$
$458$			1485.09i			3.24256i
$459$			366.898i			0.799343i
$460$	−224.259			−0.487520
$461$		−	369.852i		−	0.802282i	−0.916016	−	0.401141i	$-0.868614\pi$
$461$		−	369.852i		−	0.802282i	0.916016	−	0.401141i	$-0.131386\pi$
$462$	−313.655	+	537.721i	−0.678907	+	1.16390i
$463$	89.8128			0.193980			0.0969901	−	0.995285i	$-0.469078\pi$
$463$	89.8128			0.193980			0.0969901	+	0.995285i	$0.469078\pi$
$464$		−	63.9659i		−	0.137858i
$465$	381.753			0.820975
$466$	474.919			1.01914
$467$	−570.646			−1.22194			−0.610970	−	0.791654i	$-0.709220\pi$
$467$	−570.646			−1.22194			−0.610970	+	0.791654i	$0.709220\pi$
$468$		−	62.4870i		−	0.133519i
$469$		−	887.941i		−	1.89326i
$470$		−	1353.90i		−	2.88064i
$471$	345.077			0.732647
$472$			402.003i			0.851701i
$473$	−270.431	−	157.744i	−0.571735	−	0.333496i
$474$	848.967			1.79107
$475$			76.7770i			0.161636i
$476$	−720.914			−1.51452
$477$	−296.401			−0.621386
$478$	1128.69			2.36129
$479$		−	450.511i		−	0.940523i	−0.882527	−	0.470262i	$-0.844160\pi$
$479$		−	450.511i		−	0.940523i	0.882527	−	0.470262i	$-0.155840\pi$
$480$		−	63.2048i		−	0.131677i
$481$			0.877794i			0.00182494i
$482$	−521.249			−1.08143
$483$		−	78.9245i		−	0.163405i
$484$	466.113	+	824.203i	0.963043	+	1.70290i
$485$	186.783			0.385119
$486$		−	667.564i		−	1.37359i
$487$	−322.907			−0.663054			−0.331527	−	0.943446i	$-0.607564\pi$
$487$	−322.907			−0.663054			−0.331527	+	0.943446i	$0.607564\pi$
$488$	189.131			0.387564
$489$	−324.542			−0.663685
$490$		−	91.1565i		−	0.186034i
$491$			178.686i			0.363923i	0.983306	+	0.181962i	$0.0582447\pi$
$491$			178.686i			0.363923i	−0.983306	+	0.181962i	$0.941755\pi$
$492$			969.598i			1.97073i
$493$	−57.8481			−0.117339
$494$		−	50.0786i		−	0.101374i
$495$	−130.214	+	223.235i	−0.263058	+	0.450979i
$496$	−395.449			−0.797277
$497$		−	377.032i		−	0.758616i
$498$	−938.347			−1.88423
$499$	−278.375			−0.557866			−0.278933	−	0.960311i	$-0.589981\pi$
$499$	−278.375			−0.557866			−0.278933	+	0.960311i	$0.589981\pi$
$500$	−668.336			−1.33667
$501$			121.138i			0.241793i
$502$			1235.08i			2.46033i
$503$		−	172.701i		−	0.343342i	−0.985154	−	0.171671i	$-0.945083\pi$
$503$		−	172.701i		−	0.343342i	0.985154	−	0.171671i	$-0.0549166\pi$
$504$	378.081			0.750160
$505$		−	209.614i		−	0.415078i
$506$	−156.701	−	91.4047i	−0.309686	−	0.180642i
$507$	371.181			0.732113
$508$		−	1782.05i		−	3.50798i
$509$	395.718			0.777442			0.388721	−	0.921356i	$-0.372917\pi$
$509$	395.718			0.777442			0.388721	+	0.921356i	$0.372917\pi$
$510$	583.012			1.14316
$511$	−569.089			−1.11368
$512$			798.743i			1.56005i
$513$		−	208.751i		−	0.406923i
$514$			282.531i			0.549672i
$515$	691.767			1.34324
$516$		−	501.410i		−	0.971726i
$517$	365.170	−	626.036i	0.706325	−	1.21090i
$518$	−10.8647			−0.0209743
$519$		−	288.141i		−	0.555185i
$520$	−159.649			−0.307018
$521$	199.501			0.382919			0.191460	−	0.981500i	$-0.438678\pi$
$521$	199.501			0.382919			0.191460	+	0.981500i	$0.438678\pi$
$522$	62.0611			0.118891
$523$		−	359.461i		−	0.687307i	−0.939097	−	0.343653i	$-0.888335\pi$
$523$		−	359.461i		−	0.687307i	0.939097	−	0.343653i	$-0.111665\pi$
$524$		−	1530.81i		−	2.92139i
$525$			176.212i			0.335643i
$526$	1160.54			2.20634
$527$			357.628i			0.678611i
$528$	−173.879	+	298.092i	−0.329315	+	0.564568i
$529$	23.0000			0.0434783
$530$			1549.13i			2.92288i
$531$	−120.150			−0.226272
$532$	410.173			0.771002
$533$	−111.778			−0.209714
$534$		−	497.179i		−	0.931047i
$535$			682.935i			1.27651i
$536$		−	1597.91i		−	2.98118i
$537$	−470.769			−0.876665
$538$		−	169.596i		−	0.315235i
$539$	24.5865	−	42.1503i	0.0456150	−	0.0782009i
$540$	−1361.36			−2.52104
$541$			344.221i			0.636267i	0.948046	+	0.318134i	$0.103056\pi$
$541$			344.221i			0.636267i	−0.948046	+	0.318134i	$0.896944\pi$
$542$	1329.78			2.45347
$543$	461.133			0.849232
$544$	59.2105			0.108843
$545$		−	567.806i		−	1.04185i
$546$		−	114.936i		−	0.210506i
$547$			202.651i			0.370476i	0.982694	+	0.185238i	$0.0593057\pi$
$547$			202.651i			0.370476i	−0.982694	+	0.185238i	$0.940694\pi$
$548$	−691.905			−1.26260
$549$			56.5273i			0.102964i
$550$	349.862	+	204.076i	0.636113	+	0.371048i
$551$	32.9134			0.0597340
$552$		−	142.030i		−	0.257301i
$553$	−801.621			−1.44959
$554$	−96.8235			−0.174772
$555$	5.81436			0.0104763
$556$			429.203i			0.771948i
$557$			242.506i			0.435379i	0.976018	+	0.217689i	$0.0698519\pi$
$557$			242.506i			0.435379i	−0.976018	+	0.217689i	$0.930148\pi$
$558$		−	383.673i		−	0.687587i
$559$	57.8039			0.103406
$560$		−	608.717i		−	1.08700i
$561$	269.582	+	157.248i	0.480538	+	0.280300i
$562$	−142.818			−0.254125
$563$		−	919.697i		−	1.63357i	−0.576946	−	0.816783i	$-0.695756\pi$
$563$		−	919.697i		−	1.63357i	0.576946	−	0.816783i	$-0.304244\pi$
$564$	1160.74			2.05806
$565$	318.369			0.563485
$566$	297.029			0.524786
$567$		−	220.443i		−	0.388788i
$568$		−	678.495i		−	1.19453i
$569$		−	444.307i		−	0.780855i	−0.920634	−	0.390428i	$-0.872327\pi$
$569$		−	444.307i		−	0.780855i	0.920634	−	0.390428i	$-0.127673\pi$
$570$	−331.712			−0.581951
$571$		−	1061.89i		−	1.85970i	−0.367939	−	0.929850i	$-0.619936\pi$
$571$		−	1061.89i		−	1.85970i	0.367939	−	0.929850i	$-0.380064\pi$
$572$	−151.011	−	88.0856i	−0.264006	−	0.153996i
$573$	602.238			1.05103
$574$		−	1383.50i		−	2.41028i
$575$	−51.3514			−0.0893067
$576$	−282.682			−0.490767
$577$	−315.321			−0.546484			−0.273242	−	0.961945i	$-0.588096\pi$
$577$	−315.321			−0.546484			−0.273242	+	0.961945i	$0.588096\pi$
$578$		−	447.648i		−	0.774477i
$579$		−	427.809i		−	0.738876i
$580$		−	214.643i		−	0.370074i
$581$	886.016			1.52499
$582$			241.989i			0.415789i
$583$	−417.826	+	716.307i	−0.716682	+	1.22866i
$584$	−1024.11			−1.75362
$585$		−	47.7158i		−	0.0815655i
$586$	737.194			1.25801
$587$	772.580			1.31615			0.658075	−	0.752953i	$-0.271371\pi$
$587$	772.580			1.31615			0.658075	+	0.752953i	$0.271371\pi$
$588$	78.1516			0.132911
$589$		−	203.477i		−	0.345462i
$590$			627.959i			1.06434i
$591$		−	687.492i		−	1.16327i
$592$	−6.02296			−0.0101739
$593$		−	603.262i		−	1.01730i	−0.860972	−	0.508652i	$-0.830144\pi$
$593$		−	603.262i		−	1.01730i	0.860972	−	0.508652i	$-0.169856\pi$
$594$	−951.252	−	554.870i	−1.60143	−	0.934124i
$595$	−550.499			−0.925208
$596$		−	20.2622i		−	0.0339970i
$597$	548.975			0.919556
$598$	33.4945			0.0560109
$599$	−247.853			−0.413778			−0.206889	−	0.978364i	$-0.566334\pi$
$599$	−247.853			−0.413778			−0.206889	+	0.978364i	$0.566334\pi$
$600$			317.106i			0.528510i
$601$			873.338i			1.45314i	0.687092	+	0.726570i	$0.258887\pi$
$601$			873.338i			1.45314i	−0.687092	+	0.726570i	$0.741113\pi$
$602$			715.453i			1.18846i
$603$	477.582			0.792010
$604$			1623.05i			2.68717i
$605$	355.929	+	629.371i	0.588313	+	1.04028i
$606$	271.569			0.448134
$607$		−	354.871i		−	0.584631i	−0.956322	−	0.292315i	$-0.905574\pi$
$607$		−	354.871i		−	0.584631i	0.956322	−	0.292315i	$-0.0944257\pi$
$608$	−33.6886			−0.0554088
$609$	75.5402			0.124040
$610$	295.437			0.484323
$611$			133.814i			0.219008i
$612$		−	387.746i		−	0.633572i
$613$			700.416i			1.14260i	0.820740	+	0.571302i	$0.193562\pi$
$613$			700.416i			1.14260i	−0.820740	+	0.571302i	$0.806438\pi$
$614$	699.065			1.13854
$615$			740.397i			1.20390i
$616$	532.966	−	913.700i	0.865205	−	1.48328i
$617$	−479.487			−0.777127			−0.388563	−	0.921422i	$-0.627029\pi$
$617$	−479.487			−0.777127			−0.388563	+	0.921422i	$0.627029\pi$
$618$			896.228i			1.45021i
$619$	170.763			0.275870			0.137935	−	0.990441i	$-0.455954\pi$
$619$	170.763			0.275870			0.137935	+	0.990441i	$0.455954\pi$
$620$	−1326.96			−2.14026
$621$	139.621			0.224832
$622$			1682.70i			2.70530i
$623$			469.452i			0.753535i
$624$		−	63.7164i		−	0.102110i
$625$	−778.037			−1.24486
$626$		−	660.503i		−	1.05512i
$627$	−153.382	−	89.4684i	−0.244628	−	0.142693i
$628$	−1199.48			−1.91000
$629$			5.44691i			0.00865963i
$630$	590.590			0.937445
$631$	1034.16			1.63892			0.819462	−	0.573134i	$-0.194273\pi$
$631$	1034.16			1.63892			0.819462	+	0.573134i	$0.194273\pi$
$632$	−1442.57			−2.28255
$633$		−	630.387i		−	0.995873i
$634$			1114.47i			1.75784i
$635$		−	1360.80i		−	2.14299i
$636$	−1328.12			−2.08824
$637$			9.00951i			0.0141437i
$638$	87.4852	−	149.982i	0.137124	−	0.235081i
$639$	202.788			0.317352
$640$			1365.12i			2.13300i
$641$	−136.623			−0.213140			−0.106570	−	0.994305i	$-0.533987\pi$
$641$	−136.623			−0.213140			−0.106570	+	0.994305i	$0.533987\pi$
$642$	−884.786			−1.37817
$643$	951.295			1.47946			0.739731	−	0.672902i	$-0.234953\pi$
$643$	951.295			1.47946			0.739731	+	0.672902i	$0.234953\pi$
$644$			274.339i			0.425993i
$645$		−	382.883i		−	0.593617i
$646$		−	310.749i		−	0.481036i
$647$	414.008			0.639888			0.319944	−	0.947436i	$-0.396336\pi$
$647$	414.008			0.639888			0.319944	+	0.947436i	$0.396336\pi$
$648$		−	396.702i		−	0.612194i
$649$	−169.371	+	290.365i	−0.260973	+	0.447403i
$650$	−74.7821			−0.115049
$651$		−	467.004i		−	0.717364i
$652$	1128.10			1.73021
$653$	−756.063			−1.15783			−0.578915	−	0.815388i	$-0.696524\pi$
$653$	−756.063			−1.15783			−0.578915	+	0.815388i	$0.696524\pi$
$654$	735.630			1.12482
$655$		−	1168.94i		−	1.78464i
$656$		−	766.960i		−	1.16915i
$657$		−	306.086i		−	0.465885i
$658$	−1656.24			−2.51709
$659$			555.152i			0.842415i	0.906964	+	0.421208i	$0.138394\pi$
$659$			555.152i			0.842415i	−0.906964	+	0.421208i	$0.861606\pi$
$660$	−583.464	+	1000.27i	−0.884036	+	1.51556i
$661$	−256.614			−0.388220			−0.194110	−	0.980980i	$-0.562182\pi$
$661$	−256.614			−0.388220			−0.194110	+	0.980980i	$0.562182\pi$
$662$			2194.02i			3.31423i
$663$	−57.6224			−0.0869116
$664$	1594.45			2.40128
$665$	313.213			0.470997
$666$		−	5.84360i		−	0.00877417i
$667$			22.0138i			0.0330041i
$668$		−	421.073i		−	0.630348i
$669$	−668.949			−0.999923
$670$		−	2496.06i		−	3.72546i
$671$	136.609	+	79.6844i	0.203589	+	0.118755i
$672$	−77.3193			−0.115058
$673$			491.131i			0.729763i	0.931054	+	0.364882i	$0.118891\pi$
$673$			491.131i			0.729763i	−0.931054	+	0.364882i	$0.881109\pi$
$674$	−16.3976			−0.0243288
$675$	−311.727			−0.461818
$676$	−1290.22			−1.90860
$677$		−	700.792i		−	1.03514i	−0.855640	−	0.517572i	$-0.826836\pi$
$677$		−	700.792i		−	1.03514i	0.855640	−	0.517572i	$-0.173164\pi$
$678$			412.468i			0.608359i
$679$		−	228.494i		−	0.336515i
$680$	−990.660			−1.45685
$681$			561.192i			0.824070i
$682$	−927.216	−	540.850i	−1.35955	−	0.793035i
$683$	328.837			0.481460			0.240730	−	0.970592i	$-0.422613\pi$
$683$	328.837			0.481460			0.240730	+	0.970592i	$0.422613\pi$
$684$			220.613i			0.322534i
$685$	−528.347			−0.771310
$686$	1120.23			1.63299
$687$	−972.247			−1.41521
$688$			396.620i			0.576482i
$689$		−	153.109i		−	0.222219i
$690$		−	221.862i		−	0.321539i
$691$	−863.102			−1.24906			−0.624531	−	0.781000i	$-0.714710\pi$
$691$	−863.102			−1.24906			−0.624531	+	0.781000i	$0.714710\pi$
$692$			1001.57i			1.44736i
$693$	273.086	+	159.292i	0.394063	+	0.229859i
$694$	−1219.73			−1.75754
$695$			327.745i			0.471575i
$696$	135.940			0.195316
$697$	−693.606			−0.995131
$698$	1935.43			2.77282
$699$			310.915i			0.444800i
$700$		−	612.509i		−	0.875013i
$701$			44.9150i			0.0640728i	0.999487	+	0.0320364i	$0.0101992\pi$
$701$			44.9150i			0.0640728i	−0.999487	+	0.0320364i	$0.989801\pi$
$702$	203.328			0.289640
$703$		−	3.09909i		−	0.00440837i
$704$	−398.486	+	683.152i	−0.566032	+	0.970387i
$705$	886.358			1.25725
$706$		−	556.491i		−	0.788230i
$707$	−256.424			−0.362693
$708$	−538.370			−0.760410
$709$	−800.428			−1.12895			−0.564477	−	0.825449i	$-0.690922\pi$
$709$	−800.428			−1.12895			−0.564477	+	0.825449i	$0.690922\pi$
$710$		−	1059.86i		−	1.49276i
$711$		−	431.155i		−	0.606406i
$712$			844.811i			1.18653i
$713$	136.093			0.190874
$714$		−	713.206i		−	0.998889i
$715$	−115.314	−	67.2632i	−0.161278	−	0.0940744i
$716$	1636.38			2.28545
$717$			738.923i			1.03058i
$718$	1396.22			1.94460
$719$	177.690			0.247134			0.123567	−	0.992336i	$-0.460567\pi$
$719$	177.690			0.247134			0.123567	+	0.992336i	$0.460567\pi$
$720$	327.401			0.454723
$721$		−	846.247i		−	1.17371i
$722$		−	1064.61i		−	1.47452i
$723$		−	341.246i		−	0.471987i
$724$	−1602.88			−2.21393
$725$		−	49.1494i		−	0.0677923i
$726$	−815.391	+	461.130i	−1.12313	+	0.635165i
$727$	−323.317			−0.444727			−0.222364	−	0.974964i	$-0.571377\pi$
$727$	−323.317			−0.444727			−0.222364	+	0.974964i	$0.571377\pi$
$728$			195.301i			0.268271i
$729$	708.441			0.971798
$730$	−1599.74			−2.19143
$731$	358.686			0.490679
$732$			253.288i			0.346022i
$733$			737.211i			1.00575i	0.864361	+	0.502873i	$0.167723\pi$
$733$			737.211i			1.00575i	−0.864361	+	0.502873i	$0.832277\pi$
$734$		−	1903.00i		−	2.59265i
$735$	59.6775			0.0811938
$736$		−	22.5322i		−	0.0306144i
$737$	673.229	−	1154.16i	0.913473	−	1.56603i
$738$	744.120			1.00829
$739$		−	1055.37i		−	1.42811i	−0.700090	−	0.714055i	$-0.746857\pi$
$739$		−	1055.37i		−	1.42811i	0.700090	−	0.714055i	$-0.253143\pi$
$740$	−20.2105			−0.0273115
$741$	32.7850			0.0442442
$742$	1895.07			2.55400
$743$			777.241i			1.04608i	0.852307	+	0.523042i	$0.175203\pi$
$743$			777.241i			1.04608i	−0.852307	+	0.523042i	$0.824797\pi$
$744$		−	840.406i		−	1.12958i
$745$		−	15.4725i		−	0.0207684i
$746$	1279.11			1.71463
$747$			476.547i			0.637948i
$748$	−937.058	−	546.591i	−1.25275	−	0.730737i
$749$	835.443			1.11541
$750$		−	661.191i		−	0.881588i
$751$	−973.248			−1.29594			−0.647968	−	0.761668i	$-0.724381\pi$
$751$	−973.248			−1.29594			−0.647968	+	0.761668i	$0.724381\pi$
$752$	−918.158			−1.22096
$753$	−808.572			−1.07380
$754$			32.0582i			0.0425176i
$755$			1239.38i			1.64157i
$756$			1665.37i			2.20287i
$757$	623.216			0.823271			0.411635	−	0.911349i	$-0.364958\pi$
$757$	623.216			0.823271			0.411635	+	0.911349i	$0.364958\pi$
$758$			1363.24i			1.79847i
$759$	59.8399	−	102.588i	0.0788405	−	0.135162i
$760$	563.648			0.741643
$761$		−	547.492i		−	0.719437i	−0.933061	−	0.359719i	$-0.882873\pi$
$761$		−	547.492i		−	0.719437i	0.933061	−	0.359719i	$-0.117127\pi$
$762$	1763.00			2.31365
$763$	−694.605			−0.910360
$764$	−2093.36			−2.74000
$765$		−	296.088i		−	0.387042i
$766$		−	1056.55i		−	1.37931i
$767$		−	62.0647i		−	0.0809188i
$768$	−1121.15			−1.45983
$769$			992.816i			1.29105i	0.763740	+	0.645524i	$0.223361\pi$
$769$			992.816i			1.29105i	−0.763740	+	0.645524i	$0.776639\pi$
$770$	832.533	−	1427.27i	1.08121	−	1.85360i
$771$	−184.965			−0.239903
$772$			1487.05i			1.92623i
$773$	−165.000			−0.213454			−0.106727	−	0.994288i	$-0.534037\pi$
$773$	−165.000			−0.213454			−0.106727	+	0.994288i	$0.534037\pi$
$774$	−384.809			−0.497169
$775$	−303.851			−0.392066
$776$		−	411.190i		−	0.529885i
$777$		−	7.11278i		−	0.00915415i
$778$			1765.32i			2.26905i
$779$	394.636			0.506593
$780$		−	213.806i		−	0.274110i
$781$	285.863	−	490.074i	0.366021	−	0.627496i
$782$	207.841			0.265781
$783$			133.634i			0.170669i
$784$	−61.8185			−0.0788501
$785$	−915.935			−1.16680
$786$	1514.44			1.92677
$787$		−	1300.19i		−	1.65208i	−0.563611	−	0.826040i	$-0.690588\pi$
$787$		−	1300.19i		−	1.65208i	0.563611	−	0.826040i	$-0.309412\pi$
$788$			2389.70i			3.03262i
$789$			759.769i			0.962952i
$790$	−2253.41			−2.85242
$791$		−	389.465i		−	0.492370i
$792$	491.437	+	286.658i	0.620501	+	0.361941i
$793$	−29.1997			−0.0368218
$794$		−	962.158i		−	1.21179i
$795$	−1014.17			−1.27568
$796$	−1908.22			−2.39726
$797$	1203.79			1.51040			0.755201	−	0.655494i	$-0.227539\pi$
$797$	1203.79			1.51040			0.755201	+	0.655494i	$0.227539\pi$
$798$			405.788i			0.508506i
$799$			830.344i			1.03923i
$800$			50.3069i			0.0628837i
$801$	−252.496			−0.315227
$802$			2493.07i			3.10857i
$803$	−739.713	−	431.478i	−0.921187	−	0.537333i
$804$	2139.95			2.66163
$805$			209.489i			0.260235i
$806$	198.190			0.245893
$807$	111.030			0.137583
$808$	−461.453			−0.571105
$809$			1206.32i			1.49113i	0.666434	+	0.745564i	$0.267820\pi$
$809$			1206.32i			1.49113i	−0.666434	+	0.745564i	$0.732180\pi$
$810$		−	619.678i		−	0.765034i
$811$			67.3561i			0.0830532i	0.999137	+	0.0415266i	$0.0132221\pi$
$811$			67.3561i			0.0830532i	−0.999137	+	0.0415266i	$0.986778\pi$
$812$	−262.576			−0.323369
$813$			870.568i			1.07081i
$814$	−14.1221	−	8.23750i	−0.0173490	−	0.0101198i
$815$	861.430			1.05697
$816$		−	395.374i		−	0.484528i
$817$	−204.079			−0.249791
$818$	199.047			0.243334
$819$	−58.3714			−0.0712715
$820$		−	2573.60i		−	3.13853i
$821$		−	327.635i		−	0.399068i	−0.979891	−	0.199534i	$-0.936057\pi$
$821$		−	327.635i		−	0.399068i	0.979891	−	0.199534i	$-0.0639428\pi$
$822$		−	684.508i		−	0.832735i
$823$	−411.970			−0.500571			−0.250285	−	0.968172i	$-0.580524\pi$
$823$	−411.970			−0.500571			−0.250285	+	0.968172i	$0.580524\pi$
$824$		−	1522.88i		−	1.84816i
$825$	−133.603	+	229.044i	−0.161943	+	0.277630i
$826$	768.190			0.930012
$827$			1084.04i			1.31081i	0.755279	+	0.655403i	$0.227501\pi$
$827$			1084.04i			1.31081i	−0.755279	+	0.655403i	$0.772499\pi$
$828$	−147.554			−0.178206
$829$	1141.88			1.37742			0.688708	−	0.725039i	$-0.258178\pi$
$829$	1141.88			1.37742			0.688708	+	0.725039i	$0.258178\pi$
$830$	2490.65			3.00078
$831$		−	63.3875i		−	0.0762785i
$832$		−	146.022i		−	0.175507i
$833$			55.9061i			0.0671141i
$834$	−424.614			−0.509130
$835$		−	321.536i		−	0.385073i
$836$	533.151	+	310.990i	0.637741	+	0.371997i
$837$	826.150			0.987037
$838$			1743.05i			2.08002i
$839$	450.554			0.537013			0.268507	−	0.963278i	$-0.413470\pi$
$839$	450.554			0.537013			0.268507	+	0.963278i	$0.413470\pi$
$840$	1293.64			1.54005
$841$	819.930			0.974947
$842$			1265.19i			1.50260i
$843$		−	93.4990i		−	0.110912i
$844$			2191.21i			2.59622i
$845$	−985.224			−1.16595
$846$		−	890.816i		−	1.05297i
$847$	769.918	−	435.413i	0.908994	−	0.514065i
$848$	1050.55			1.23886
$849$			194.456i			0.229041i
$850$	−464.040			−0.545929
$851$	2.07279			0.00243571
$852$	908.655			1.06650
$853$		−	1062.60i		−	1.24572i	−0.782334	−	0.622859i	$-0.785971\pi$
$853$		−	1062.60i		−	1.24572i	0.782334	−	0.622859i	$-0.214029\pi$
$854$		−	361.412i		−	0.423199i
$855$			168.463i			0.197032i
$856$	1503.44			1.75635
$857$		−	1491.67i		−	1.74057i	−0.492550	−	0.870284i	$-0.663935\pi$
$857$		−	1491.67i		−	1.74057i	0.492550	−	0.870284i	$-0.336065\pi$
$858$	87.1438	−	149.397i	0.101566	−	0.174122i
$859$	−462.413			−0.538315			−0.269158	−	0.963096i	$-0.586745\pi$
$859$	−462.413			−0.538315			−0.269158	+	0.963096i	$0.586745\pi$
$860$			1330.89i			1.54755i
$861$	905.737			1.05196
$862$	1936.52			2.24654
$863$	−606.226			−0.702464			−0.351232	−	0.936289i	$-0.614237\pi$
$863$	−606.226			−0.702464			−0.351232	+	0.936289i	$0.614237\pi$
$864$		−	136.781i		−	0.158312i
$865$			764.811i			0.884174i
$866$			1377.05i			1.59013i
$867$	293.062			0.338018
$868$			1623.29i			1.87015i
$869$	−1041.96	−	607.783i	−1.19904	−	0.699405i
$870$	212.348			0.244078
$871$			246.699i			0.283237i
$872$	−1249.99			−1.43347
$873$	122.896			0.140775
$874$	−118.254			−0.135302
$875$			624.317i			0.713505i
$876$		−	1371.51i		−	1.56566i
$877$			568.547i			0.648287i	0.946008	+	0.324143i	$0.105076\pi$
$877$			568.547i			0.648287i	−0.946008	+	0.324143i	$0.894924\pi$
$878$	176.826			0.201396
$879$			482.619i			0.549055i
$880$	461.525	−	791.223i	0.524460	−	0.899117i
$881$	202.445			0.229790			0.114895	−	0.993378i	$-0.463347\pi$
$881$	202.445			0.229790			0.114895	+	0.993378i	$0.463347\pi$
$882$		−	59.9776i		−	0.0680018i
$883$	877.269			0.993510			0.496755	−	0.867891i	$-0.334525\pi$
$883$	877.269			0.993510			0.496755	+	0.867891i	$0.334525\pi$
$884$	200.294			0.226577
$885$	−411.106			−0.464526
$886$			668.351i			0.754346i
$887$		−	1317.64i		−	1.48550i	−0.669568	−	0.742751i	$-0.733521\pi$
$887$		−	1317.64i		−	1.48550i	0.669568	−	0.742751i	$-0.266479\pi$
$888$		−	12.7999i		−	0.0144143i
$889$	−1664.68			−1.87253
$890$			1319.66i			1.48276i
$891$	167.138	−	286.536i	0.187584	−	0.321589i
$892$	2325.25			2.60678
$893$		−	472.434i		−	0.529042i
$894$	20.0456			0.0224224
$895$	1249.56			1.39615
$896$	1669.97			1.86381
$897$			21.9279i			0.0244458i
$898$		−	1175.14i		−	1.30862i
$899$			130.257i			0.144891i
$900$	329.440			0.366045
$901$		−	950.075i		−	1.05447i
$902$	1048.96	−	1798.30i	1.16292	−	1.99368i
$903$	−468.386			−0.518700
$904$		−	700.869i		−	0.775297i
$905$	−1223.98			−1.35247
$906$	−1605.70			−1.77230
$907$	757.738			0.835433			0.417716	−	0.908577i	$-0.362831\pi$
$907$	757.738			0.835433			0.417716	+	0.908577i	$0.362831\pi$
$908$		−	1950.69i		−	2.14833i
$909$		−	137.919i		−	0.151726i
$910$			305.075i			0.335247i
$911$	−375.430			−0.412107			−0.206054	−	0.978541i	$-0.566062\pi$
$911$	−375.430			−0.412107			−0.206054	+	0.978541i	$0.566062\pi$
$912$			224.953i			0.246659i
$913$	1151.66	+	671.770i	1.26140	+	0.735783i
$914$	−1020.59			−1.11662
$915$			193.414i			0.211381i
$916$	3379.50			3.68941
$917$	−1429.98			−1.55941
$918$	1261.69			1.37439
$919$		−	724.408i		−	0.788257i	−0.919055	−	0.394129i	$-0.871046\pi$
$919$		−	724.408i		−	0.788257i	0.919055	−	0.394129i	$-0.128954\pi$
$920$			376.990i			0.409771i
$921$			457.657i			0.496914i
$922$	−1271.85			−1.37945
$923$			104.752i			0.113491i
$924$	1223.65	+	713.759i	1.32429	+	0.772466i
$925$	−4.62785			−0.00500308
$926$		−	308.849i		−	0.333530i
$927$	455.157			0.491000
$928$	21.5660			0.0232392
$929$	−1279.10			−1.37685			−0.688427	−	0.725305i	$-0.741699\pi$
$929$	−1279.10			−1.37685			−0.688427	+	0.725305i	$0.741699\pi$
$930$		−	1312.78i		−	1.41159i
$931$		−	31.8085i		−	0.0341659i
$932$		−	1080.73i		−	1.15958i
$933$	−1101.61			−1.18072
$934$			1962.34i			2.10101i
$935$	−715.549	−	417.383i	−0.765293	−	0.446399i
$936$	−105.043			−0.112226
$937$			212.460i			0.226745i	0.993553	+	0.113373i	$0.0361654\pi$
$937$			212.460i			0.226745i	−0.993553	+	0.113373i	$0.963835\pi$
$938$	−3053.46			−3.25529
$939$	432.412			0.460502
$940$	−3080.96			−3.27761
$941$			587.395i			0.624224i	0.950045	+	0.312112i	$0.101036\pi$
$941$			587.395i			0.624224i	−0.950045	+	0.312112i	$0.898964\pi$
$942$		−	1186.65i		−	1.25972i
$943$			263.948i			0.279902i
$944$	425.855			0.451118
$945$			1271.70i			1.34571i
$946$	−542.450	+	929.960i	−0.573415	+	0.983044i
$947$	−1351.22			−1.42684			−0.713419	−	0.700737i	$-0.752854\pi$
$947$	−1351.22			−1.42684			−0.713419	+	0.700737i	$0.752854\pi$
$948$		−	1931.92i		−	2.03789i
$949$	158.112			0.166609
$950$	264.021			0.277917
$951$	−729.609			−0.767202
$952$			1211.89i			1.27299i
$953$		−	1465.42i		−	1.53769i	−0.639434	−	0.768846i	$-0.720831\pi$
$953$		−	1465.42i		−	1.53769i	0.639434	−	0.768846i	$-0.279169\pi$
$954$			1019.27i			1.06841i
$955$	−1598.52			−1.67384
$956$		−	2568.47i		−	2.68669i
$957$	98.1887	+	57.2740i	0.102601	+	0.0598474i
$958$	−1549.22			−1.61714
$959$			646.334i			0.673967i
$960$	−967.225			−1.00753
$961$	−155.724			−0.162044
$962$	3.01857			0.00313780
$963$			449.346i			0.466610i
$964$			1186.16i			1.23046i
$965$			1135.53i			1.17672i
$966$	−271.406			−0.280959
$967$		−	561.539i		−	0.580702i	−0.956920	−	0.290351i	$-0.906228\pi$
$967$		−	561.539i		−	0.580702i	0.956920	−	0.290351i	$-0.0937721\pi$
$968$	1385.52	−	783.556i	1.43132	−	0.809458i
$969$	203.438			0.209947
$970$		−	642.311i		−	0.662176i
$971$	−1303.88			−1.34282			−0.671409	−	0.741087i	$-0.734310\pi$
$971$	−1303.88			−1.34282			−0.671409	+	0.741087i	$0.734310\pi$
$972$	−1519.12			−1.56288
$973$	400.934			0.412060
$974$			1110.42i			1.14006i
$975$		−	48.9576i		−	0.0502130i
$976$		−	200.353i		−	0.205280i
$977$	787.476			0.806014			0.403007	−	0.915197i	$-0.367965\pi$
$977$	787.476			0.806014			0.403007	+	0.915197i	$0.367965\pi$
$978$			1116.04i			1.14114i
$979$	−355.935	+	610.203i	−0.363570	+	0.623293i
$980$	−207.437			−0.211671
$981$		−	373.596i		−	0.380831i
$982$	614.468			0.625731
$983$	281.156			0.286018			0.143009	−	0.989721i	$-0.454322\pi$
$983$	281.156			0.286018			0.143009	+	0.989721i	$0.454322\pi$
$984$	1629.94			1.65644
$985$			1824.81i			1.85259i
$986$			198.929i			0.201753i
$987$		−	1084.29i		−	1.09858i
$988$	−113.960			−0.115344
$989$		−	136.496i		−	0.138014i
$990$	767.661	+	447.781i	0.775416	+	0.452304i
$991$	943.116			0.951681			0.475840	−	0.879532i	$-0.342144\pi$
$991$	943.116			0.951681			0.475840	+	0.879532i	$0.342144\pi$
$992$		−	133.325i		−	0.134400i
$993$	−1436.36			−1.44648
$994$	−1296.54			−1.30437
$995$	−1457.14			−1.46446
$996$			2135.32i			2.14389i
$997$		−	645.342i		−	0.647284i	−0.946180	−	0.323642i	$-0.895093\pi$
$997$		−	645.342i		−	0.647284i	0.946180	−	0.323642i	$-0.104907\pi$
$998$			957.279i			0.959198i
$999$	12.5828			0.0125954

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	253.3.c.a.208.4	✓	44
11.10	odd	2	inner	253.3.c.a.208.41	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.3.c.a.208.4	✓	44	1.1	even	1	trivial
253.3.c.a.208.41	yes	44	11.10	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 253 = 11 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	253.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.43881i q^{2} +2.25129 q^{3} -7.82541 q^{4} -5.97558 q^{5} -7.74175i q^{6} +7.31000i q^{7} +13.1548i q^{8} -3.93171 q^{9} +20.5489i q^{10} +(-5.54238 + 9.50168i) q^{11} -17.6172 q^{12} -2.03096i q^{13} +25.1377 q^{14} -13.4527 q^{15} +13.9354 q^{16} -12.6026i q^{17} +13.5204i q^{18} +7.17039i q^{19} +46.7613 q^{20} +16.4569i q^{21} +(32.6745 + 19.0592i) q^{22} -4.79583 q^{23} +29.6153i q^{24} +10.7075 q^{25} -6.98408 q^{26} -29.1130 q^{27} -57.2037i q^{28} -4.59018i q^{29} +46.2614i q^{30} -28.3774 q^{31} +4.69829i q^{32} +(-12.4775 + 21.3910i) q^{33} -43.3378 q^{34} -43.6815i q^{35} +30.7672 q^{36} -0.432206 q^{37} +24.6576 q^{38} -4.57227i q^{39} -78.6078i q^{40} -55.0369i q^{41} +56.5921 q^{42} +28.4614i q^{43} +(43.3714 - 74.3546i) q^{44} +23.4942 q^{45} +16.4919i q^{46} -65.8869 q^{47} +31.3725 q^{48} -4.43608 q^{49} -36.8211i q^{50} -28.3720i q^{51} +15.8931i q^{52} +75.3874 q^{53} +100.114i q^{54} +(33.1189 - 56.7780i) q^{55} -96.1619 q^{56} +16.1426i q^{57} -15.7848 q^{58} +30.5593 q^{59} +105.273 q^{60} -14.3773i q^{61} +97.5844i q^{62} -28.7408i q^{63} +71.8980 q^{64} +12.1362i q^{65} +(73.5596 + 42.9077i) q^{66} -121.469 q^{67} +98.6202i q^{68} -10.7968 q^{69} -150.212 q^{70} -51.5776 q^{71} -51.7210i q^{72} +77.8507i q^{73} +1.48627i q^{74} +24.1057 q^{75} -56.1112i q^{76} +(-69.4573 - 40.5148i) q^{77} -15.7232 q^{78} +109.661i q^{79} -83.2719 q^{80} -30.1563 q^{81} -189.261 q^{82} -121.206i q^{83} -128.782i q^{84} +75.3076i q^{85} +97.8732 q^{86} -10.3338i q^{87} +(-124.993 - 72.9092i) q^{88} +64.2205 q^{89} -80.7921i q^{90} +14.8463 q^{91} +37.5293 q^{92} -63.8856 q^{93} +226.572i q^{94} -42.8472i q^{95} +10.5772i q^{96} -31.2577 q^{97} +15.2548i q^{98} +(21.7910 - 37.3579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 8 q^{3} - 88 q^{4} + 100 q^{9} + 8 q^{14} - 8 q^{15} + 72 q^{16} - 40 q^{20} - 76 q^{22} + 268 q^{25} - 40 q^{26} + 32 q^{27} + 72 q^{31} - 90 q^{33} + 60 q^{34} - 312 q^{36} + 4 q^{37} + 40 q^{38}+ \cdots + 494 q^{99}+O(q^{100}) \) 44 * q + 8 * q^3 - 88 * q^4 + 100 * q^9 + 8 * q^14 - 8 * q^15 + 72 * q^16 - 40 * q^20 - 76 * q^22 + 268 * q^25 - 40 * q^26 + 32 * q^27 + 72 * q^31 - 90 * q^33 + 60 * q^34 - 312 * q^36 + 4 * q^37 + 40 * q^38 + 12 * q^42 + 186 * q^44 - 180 * q^45 - 72 * q^47 + 252 * q^48 - 464 * q^49 + 100 * q^53 - 48 * q^55 + 208 * q^56 - 148 * q^58 - 144 * q^59 - 324 * q^60 - 416 * q^64 - 238 * q^66 + 292 * q^67 + 540 * q^70 + 544 * q^71 - 236 * q^75 + 64 * q^77 - 344 * q^78 + 156 * q^80 - 404 * q^81 + 72 * q^82 - 136 * q^86 + 608 * q^88 - 80 * q^89 - 4 * q^91 - 372 * q^93 + 68 * q^97 + 494 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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